基于极大似然的异方差多正态总体均值的参数Bootstrap检验  

A Parametric Bootstrap Test Based on Maximum Likelihood for the Equality of Several Normal Group Means with Unequal Variances

作　　者：梅波[1] 徐礼文[1,2] 

机构地区：[1]中国人民大学统计学院,北京100872 [2]北方工业大学理学院,北京100144

出　　处：《数理统计与管理》2016年第4期630-640,共11页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(11171002);北京市属高等学校高层次人才引进与培养计划项目(CIT&TCD201404002)

摘　　要：本文考虑了异方差下多正态总体均值的检验问题。传统检验方法多为近似分布检验,且受总体数目及其样本量的影响较为严重,只有在总体数目较少、样本量适中或较大时才能很好的控制第一类错误。较近提出的参数bootstrap检验有效解决了在总体数目较多时检验的任意性,但在总体样本量都较小时,检验控制第一类错误倾向保守,或总体中存在个别样本量较少时犯第一类错误概率上升。本文从极大似然的角度推导出具有修正权重的极大似然检验统计量,并与bootstrap方法有效的结合,得到新的参数bootstrap检验方法。通过Monte Carlo模拟第一类错误和检验的势与Welch检验和广义F检验进行比较,结果表明本文提出的极大似然参数bootstrap检验在总体数目较多和存在小样本量时,均能很好地控制第一类错误,同时且有较好的势,适用范围更加广泛。This article is about testing the equality of several normal means when the variances are unknown and arbitrary. Most of the conventional relevant tests are correlated with asymptotic procedure which could be seriously affected by the number of populations and sample sizes. These kind asymptotic solutions perform satisfactorily in terms of Type I errors only when sample sizes are large and the number of means to be compared is small. Even though the recent suggested parametric bootstrap approach alleviate the arbitrary of Type I errors aroused by the number of groups, the Type I errors of the test is conservative when the samples sizes are all small or is beyond the nominal level when a few of sample sizes is small. In this article, based on maximum likelihood method, we deduce a ML statistics characterized with modified weights and then combing with bootstrap method, we propose a new parametric bootstrap （PB） test.Comparing it with existed Welch test and generalized F （CF） test by Monte Carlo simulationwith respect to Type I error rates and powers, it shows the new ML PB test performs very satisfactorily even for small samples and many populations, which could be applied to much more extensive parametric range.

关 键 词：异方差 极大似然 bootstrap重抽样 Welch检验 广义F检验 

分 类 号：O212[理学—概率论与数理统计]